Bayesian inference for transductive learning of kernel matrix using the Tanner-Wong data augmentation algorithm

Zhihua Zhang, Dit-Yan Yeung, James T. Kwok

Abstract: In kernel methods, an interesting recent development seeks to learn a good kernel from empirical data automatically. In this paper, by regarding the transductive learning of the kernel matrix as a missing data problem, we propose a Bayesian hierarchical model for the problem and devise the Tanner-Wong data augmentation algorithm for making inference on the model. The Tanner-Wong algorithm is closely related to Gibbs sampling, and it also bears a strong resemblance to the expectation-maximization (EM) algorithm. For an efficient implementation, we propose a simplified Bayesian hierarchical model and the corresponding Tanner-Wong algorithm. We express the relationship between the kernel on the input space and the kernel on the output space as a symmetric-definite generalized eigenproblem. Based on this eigenproblem, an efficient approach to choosing the base kernel matrices is presented. The effectiveness of our Bayesian model with the Tanner-Wong algorithm is demonstrated through some classification experiments showing promising results.